Dual processes in neural network models. II. Analysis of zero-temperature fixed-point equations

For pt. I see ibid., vol.25, p.2577 (1992). The dynamics of learning in an unsupervised formulation of the Kohonen model has been shown to be equivalent to the dynamics of local order parameters in an attractor neural network with short-range Hebbian interactions and long-range anti-Hebbian interactions. The authors analyse the zero-temperature fixed-point equations of these systems. For the special case where the distribution of p-dimensional input vectors has rotational symmetry, the problem of finding the ground state is equivalent to finding the ground state of a system of p-dimensional Heisenberg spins with short-range ferromagnetic couplings and long-range anti-ferromagnetic couplings.